Controllable photonic and phononic topological state transfers in a small optomechanical lattice

We propose a scheme to achieve the photonic and the phononic state transfers via the topological protected edge channel based on a one-dimensional small optomechanical lattice. We find that the optomechanical lattice can be mapped into a Su-Schrieffer-Heeger model after eliminating the counter rotating wave terms. By dint of the edge channel of the Su-Schrieffer-Heeger model, we show that the quantum state transfer between the photonic left and the right edge states can be achieved with a high fidelity. Especially, our scheme can also achieve another phononic state transfer based on the same channel via controlling the next-nearest-neighboring interactions between the cavity fields; this is different from the previous investigations achieving only one kind of quantum state transfer. Our scheme provides a novel, to the best of our knowledge, path to switch two different kinds of quantum state transfers in a controllable way.